Related papers: Multivariate $\alpha$-molecules
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…
Spectral variability in hyperspectral images can result from factors including environmental, illumination, atmospheric and temporal changes. Its occurrence may lead to the propagation of significant estimation errors in the unmixing…
Shapelets are phase independent subsequences designed for time series classification. We propose three adaptations to the Shapelet Transform (ST) to capture multivariate features in multivariate time series classification. We create a…
As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…
The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry,…
In multivariate regression, when covariates are numerous, it is often reasonable to assume that only a small number of them has predictive information. In some medical applications for instance, it is believed that only a few genes out of…
Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…
The success of machine learning has resulted from its structured representation of data. Similar data have close internal representations as compressed codes for classification or emerged labels for clustering. We observe that the frequency…
Unsupervised machine learning, and in particular data clustering, is a powerful approach for the analysis of datasets and identification of characteristic features occurring throughout a dataset. It is gaining popularity across scientific…
Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…
Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…
Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics…
It has previously been hypothesized, and supported with some experimental evidence, that deeper representations, when well trained, tend to do a better job at disentangling the underlying factors of variation. We study the following related…
We propose new small-sphere distributional families for modeling multivariate directional data on $(\mathbb{S}^{p-1})^K$ for $p \ge 3$ and $K \ge 1$. In a special case of univariate directions in $\Re^3$, the new densities model random…
Let $\mathcal{D}$ be the dictionary of Gaussian mixtures: the functions created by affine change of variables of a single Gaussian in $n$ dimensions. $\mathcal{D}$ is used pervasively in scientific applications to a degree that…
For many complex systems the interaction of different scales is among the most interesting and challenging features. It seems not very successful to extract the physical properties in different scale regimes by the existing approaches, such…
In this paper we propose a framework inspired by interacting particle physics and devised to perform clustering on multidimensional datasets. To this end, any given dataset is modeled as an interacting particle system, under the assumption…
Learning with neural networks from a continuous stream of visual information presents several challenges due to the non-i.i.d. nature of the data. However, it also offers novel opportunities to develop representations that are consistent…
In this paper, I outline several conceptual and methodological issues related to modeling individual and group processes embedded in clustered/hierarchical data structures. We position multilevel modeling techniques within a broader set of…
Understanding how explicit theoretical features are encoded in opaque neural systems is a central challenge now common to neuroscience and AI. We introduce Metric Learning Encoding Models (MLEMs) to address this challenge most directly as a…